#include "beechtree.h"
#include <bits/stdc++.h>
#define endl "\n"
#define ll long long
using namespace std;
const ll N = 2e5 + 5;
vector<ll> g[N];
vector<int> ans;
ll c[N], p[N];
ll cnt[N], ptr[N];
bool ok;
void dfs(ll v)
{
for (ll to : g[v]) dfs(to);
set<ll> s;
for (ll to : g[v]) s.insert(c[to]);
ok &= g[v].size() == s.size();
cnt[c[v]]++;
}
vector<int> beechtree(int n, int m, vector<int> P, vector<int> C)
{
for (ll i = 1; i <= n; i++) p[i] = P[i - 1] + 1, c[i] = C[i - 1];
for (ll i = 2; i <= n; i++) g[p[i]].push_back(i);
{
vector<ll> b;
for (ll i = 1; i <= n; i++) b.push_back(c[i]);
sort(b.begin(), b.end());
b.resize(unique(b.begin(), b.end()) - b.begin());
for (ll i = 1; i <= n; i++) c[i] = lower_bound(b.begin(), b.end(), c[i]) - b.begin();
m = b.size() - 1;
}
for (ll i = 1; i <= n; i++)
{
priority_queue<array<ll, 3>> q;
q.push({(ll)g[i].size(), 0, i});
ll cur = 0;
for (ll j = 1; j <= m; j++) cnt[j] = 0;
ok = true;
dfs(i);
cnt[c[i]]--;
for (ll j = 1; j <= m; j++) cur += cnt[j] > 0;
vector<ll> ord;
while (!q.empty())
{
auto [sz, id, v] = q.top();
ord.push_back(v);
q.pop();
if (sz < cur)
{
ok = false;
break;
}
for (ll to : g[v])
cur -= cnt[c[to]]-- == 1, q.push({(ll)g[i].size(), (ll)ord.size(), to});
}
if (ok)
{
for (ll v : ord)
if (v != i)
ok &= p[v] == ord[cnt[c[v]]++];
}
ans.push_back(ok);
}
return ans;
}
